The Ising Model is among the most well-studied models of statistical mechanics. One reason for this is its cornucopia of graphical representations, which allows many different angles of attack on questions pertaining to the Ising model. These are models of random graphs that tie Ising correlations to connectivities in random graphs. A natural question regarding these models of random graphs is then whether they are connected to each other apart from simply representing Ising correlation functions. In this talk, we will survey the landscape of positive answers to this question from the past twenty years and discuss how such internal connections may be used to assist in the study of the graphical representations on their own terms.
Based on various joint works with Jianping Jiang, Boris Kjær, Frederik Ravn Klausen and Peter Wildemann.